Uncertainty quantification in quantum informed ferroelectric phase field model

William S. Oates; Justin Collins

doi:10.1117/12.2084413

1 April 2015 Uncertainty quantification in quantum informed ferroelectric phase field model

William S. Oates, Justin Collins

Proceedings Volume 9432, Behavior and Mechanics of Multifunctional Materials and Composites 2015; 94320C (2015) https://doi.org/10.1117/12.2084413
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2015, San Diego, California, United States

Abstract

The uncertainty of a set of phenomenological ferroelectric phase field parameters are determined from a set of density function theory calculations. Bayesian statistics are employed and numerically implemented using the Markov Chain Monte Carlo (MCMC) technique. Computational DFT data for periodic unit cells and domain wall structures is included in the analysis to identify a broader range of phase field material parameters. This allow for determining a Landau-based stored energy function, electrostrictive coupling, and polarization gradient parameters governing domain wall energy and length. We focus on the tetragonal phase ferroelectric lead titanate which may contain 180◦ and 90◦ domains walls. The comparison of the phenomenological phase field model and DFT computations illustrate good correlations and relatively small propagation of error in prediction of the continuum stored energy function. Larger uncertainty is observed in the electrostrictive stress and domain wall predictions. The larger uncertainty in the electrostrictive parameters is reduced by decoupling the stored energy and stress computations. This leads to a factor of three reduction in the standard deviation of the electrostrictive parameters. Challenges in self-consistent prediction of domain structure energies and sizes is also discussed in light of the Bayesian statistical analysis.

Citation Download Citation

William S. Oates and Justin Collins "Uncertainty quantification in quantum informed ferroelectric phase field model", Proc. SPIE 9432, Behavior and Mechanics of Multifunctional Materials and Composites 2015, 94320C (1 April 2015); https://doi.org/10.1117/12.2084413

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